In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in un...In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.展开更多
The multivalue algebroidal functions are studied with geometric method. The difficulties of multivalue and branch points are overcome, and some theorems on normality are obtained.
In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk ...In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.展开更多
In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function el...In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.展开更多
In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-...In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.展开更多
Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（...Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（z）） = E（aj,M（z）） （j = 1,..., 2v ＋ 2k ＋ 1） holds in the angular domain Ω（θ-δ,θ-δ）, where b, aj （j = 1,..., 2v -b 2k -k 1） are complex constants. The same results axe obtained for the case that△（θ） is a Borel direction of order ∞ （or ρ（τ）） of W（z） （or M（z））.展开更多
基金supported by NNSF of China(10471048)SRFDP(20050574002)
文摘In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.
基金the National Natural Science Foundation of China (Grant No. 19971029) the Natural Science Foundation of Guangdong Province (Grant No. 990444) .
文摘The multivalue algebroidal functions are studied with geometric method. The difficulties of multivalue and branch points are overcome, and some theorems on normality are obtained.
文摘In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.
基金supported by the National Natural Science Foundation of China(11501127)Guangdong Natural Science Foundation(2015A030313628)+1 种基金the Training Plan for Outstanding Young Teachers in Higher Education of Guangdong(Yqgdufe1405)the Open Fund of the National Higher Education Quality Monitoring Data Center(Guangzhou)(G1613)
文摘In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.
基金The NSF (10471048) of Chinathe Research Fund (20050574002) for the DoctoralProgram of Higher Education
文摘In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.
基金Supported by the National Natural Science Foundation of China (Grant No. 10471048)the Research Fund of the Doctoral Program of Higher Education (Grant No. 20050574002)
文摘Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（z）） = E（aj,M（z）） （j = 1,..., 2v ＋ 2k ＋ 1） holds in the angular domain Ω（θ-δ,θ-δ）, where b, aj （j = 1,..., 2v -b 2k -k 1） are complex constants. The same results axe obtained for the case that△（θ） is a Borel direction of order ∞ （or ρ（τ）） of W（z） （or M（z））.
